Computing high precision Matrix Padé approximants

We describe a new method of computing matrix Padé approximants of series with integer data in an efficient and fraction-free way, by controlling the growth of the size of intermediate coefficients. This algorithm is applied to compute high precision Padé approximants of matrix-valued generating functions of time series. As an illustration we show that we can successfully recover from noisy equidistant sampling data a joint damped signal of four antenna, even in the presence of background signals.